Square Root Calculator › Square root of 112
Square Root of 112
√112 ≈ 10.583005
112 is not a perfect square, so √112 is an irrational number that is approximately 10.583005. In simplified radical form, √112 = 4√7.
√112 lies between √100 = 10 and √121 = 11.
| Number | 112 |
| Square root (decimal) | 10.583005 |
| Simplified radical | 4√7 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 112
112 = 2^4 × 7. This is what determines the simplified radical: for √112 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √112 = 4√7.
Estimating √112 by hand
√112 falls between √100 = 10 and √121 = 11, so it starts at 10.something. The Babylonian method refines that guess by averaging it with 112 ÷ the guess:
| Step | Estimate |
| Start | 10 |
| Step 1 | 10.6 |
| Step 2 | 10.583019 |
| Step 3 | 10.583005 |
After 3 steps the estimate is 10.583005, matching √112 ≈ 10.583005.
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Frequently asked questions
Is 112 a perfect square?
No, 112 is not a perfect square, so its square root is irrational and approximately 10.583005.
What is the square root of 112 in simplest radical form?
√112 = 4√7 in simplest radical form.